As an image reconstruction method which generates tomographic image data from projection data obtained by scanning of an X-ray CT apparatus, a Fourier transform method, a filtered back projection method, an iterative approximation method, and the like have been suggested.
In general, from the viewpoint of the calculation time, calculation precision, and the memory usage, a filtered back projection method is used. Meanwhile, in the iterative approximation method, although a sequential projection process and a back projection process are performed iteratively, the calculation time and the memory usage become problematic, there are features of noise reduction, artifact reduction, and the like. Accordingly, in recent years, for practical realization of the iterative approximation method, studies on reduction in calculation time and reduction in memory usage are in progress.
On the other hand, as a filtered back projection method in multi-slice CT, an expanded Feldkamp method or a method based on the expanded Feldkamp method is mainly used. According to this method, a reconstruction filter, such as a lamp filter or a Shelpp-Logan filter, is applied to projection data, and then a value is buried (integrated) in an image by a back projection process. As the back projection process, a ray-driven type, a pixel-driven or voxel-driven type, and a distance-driven type are known.
A distance-driven type will be simply described referring to FIG. 16.
The distance-driven type refers to a method in which the distance between a pixel boundary and a beam boundary is considered as a reference. In a back projection process of the distance-driven type, as shown in FIG. 16, when the distance between the pixel boundary and the beam boundary is scanned, a projection value is sequentially buried in pixels 104 included in a beam 102. The back projection process of the distance-driven type is disclosed in, for example, PTL 1.
In the iterative approximation method, an image which is generated by the filtered back projection method is used as an initial image, thereby achieving high-speed performance. Accordingly, even when image reconstruction is performed by the iterative approximation method, it is desirable to use the filtered back projection method in combination.
The above-described back projection process is also performed in an iterative process in the iterative approximation method. Accordingly, when the filtered back projection method and the iterative approximation method are used in combination, the back projection process of the same method is introduced, whereby it is possible to obtain a tomographic image with no difference concerning the back projection process and to achieve reduction in development cost.
In the X-ray CT apparatus, an offset (referred to as “quarter offset”) for ¼ channel in a channel direction of a detector is made, and the beam paths of data having a target phase and data having an opposing phase are deviated. As a result, it is possible to effectively improve sampling density in the channel direction of the beam. In order to obtain a high-resolution image, it should suffice that a back projection process is performed from the nearest beam including opposing data. This method is referred to as high-resolution reconstruction. The high-resolution reconstruction is a technique which is useful for head scanning (in particular, diagnosis of a microstructure, such as an inner ear).
As high-resolution conversion, an opposing insertion method or a data interpolation method is generally used. The data interpolation method is disclosed in, for example, PTL 2 and PTL 3.
From above, even when image reconstruction is performed by the iterative approximation method, it is desirable to use the filtered back projection method in combination and to introduce the back projection process of the same method. It is desirable that the back projection process can perform high-resolution reconstruction.